Bootstrapping

Bootstrappable Builds (GNU Guix focus)
bootstrapping wiki
David A. Wheeler’s Page on Fully Countering Trusting Trust through Diverse Double-Compiling (DDC) - Countering Trojan Horse attacks on Compilers (Note: Requires trustworthy bootstrap compiler(s) as starting point)
Mike Stute's answer to What is a coder's worst nightmare?
research!rsc: Running the “Reflections on Trusting Trust” Compiler: This notably contains the code that Ken Thomspon used together with explainations

Reasons

Security: See Ken Thompson Really Did Launch His "Trusting Trust" Trojan Attack in Real Life. And Reflections on Rusting Trust: Proof of Concept, backdooring The One True Rust Compiler.
Portability: Binary executables have much higher bitrot than source code and keeping obsolete binary interfaces often means keeping known security issues.
Maintainability: By making sure someone else can actually continue maintaining the software, canonical versions or forks
Reproducibility's other side of the coin: One of reproducibility's effect is allowing to audit source code instead of binaries, but said source code needs to be actually used.

Tools

deblob: Remove known binary executable formats (including bytecode), designed to be fast enough to barely impact distro-scale package building performance, cannot detect all blobs
Debian's suspicious-source script: Lists what isn't present in a list of source code formats, good for manual audits. Python+magic(5) means it is quite slow.

Problematic software

Erlang

Documented as originally implemented in prolog, now version n requires binaries version n-1 or n to build. No alternative compiler known so far.

Rust

There is mrustc but it's quite unstable and so far GuixSD seems to be the only distro using it. Getting to stable also involves compiling the intermediary versions. Rustc also vendors several other projects like LLVM and rust crates (enjoy non-installable libraries), similarly to other rust software.

GCC Rust Frontend is also not ready yet (2023-03) for userland, as cargo doesn't bootstraps…

Cargo

As if rustc not bootstrapping wouldn't be enough, cargo, the buildsystem+dependency-installer for Rust software depends on ~60 direct libraries, notably including 2+ git libraries, HTTP Authentication, OpenSSL.
Cargo isn't a buildsystem, it's a full blown package manager, supply chain troublemaker (via designed-vulnerable crates.io), …

It really ought to be replaced by something which only takes care of building code (or even just generating a Makefile or a build.ninja file), as was done in the C ecosystem many times in the past (pkg-config ⇒ pkgconf, ninja ⇒ samurai, …).
This isn't a system that scales, this is just creating a gigantic blob of software that cannot be reasonably audited, right in the toolchain.

Java

Requires compilers abandonned ~10 years ago, currently doesn't builds to OpenJDK for me.

Free-Pascal Compiler / Object Pascal

Aesop seems to still be at the vaporware stage, no code is available.

Nim

The transpiled C non-source code used for bootstrapping contained in ./c_code/ is pretty much what you would get with C++ mangled symbols auto-decompiled to C.
Bootstrapping Nim via historical releases would need a bootstrap path for Object Pascal, which doesn't exists (yet?), another way would be to have a minimal Nim compiler written in another language which is capable of compiling the current compiler.

QEMU

QEMU 7.0 needs a quick fix on the pc-bios/meson.build file so you can choose to not use the binaries it ships, fixed in QEMU 7.1.
They are still required so it means identifying the source of all of them and having proper from-source packaging, it's already done in gentoo for Seabios and EDK2-OVMF (UEFI) which is enough to boot machines but not for full-x86 support, non-x86 being even more problematic (ie. which upstream is used for OpenBIOS/OpenFirmware as used for sparc32, sparc64 and ppc32).

wine-mono

In gentoo it's a collection of binaries. Upstream repository is at https://github.com/madewokherd/wine-mono but still includes binaries…

mono / .NET

Source-only building is unsupported and nearly impossible (massive chain + intermediary unstable versions).
Should also be noted that Mono started itself with the Microsoft C# compiler (History | Mono) instead of dotGNU (which is dead since 2012).

Chez Scheme

Requires bootstrap files, GNU GuixSD packaging doesn't seems to have it figured out yet.

NekoVM

Doesn't seems possible to build without boot/*.n files being present, which are NekoVM bytecode files.

Not Quite Perl (NQP)

Doesn't seems possible to build without src/vm/moar/stage0/*.moarvm files being present, which are MoarVM bytecode files. This means no Rakudo/Perl6.

GNU gnulib

lib/javaversion.class. Made [PATCH] lib/javaversion.class: Remove, build from source to have it built from source.

GNU gettext

gnulib java blob; 3 Java class files in gettext-tools/examples; gettext-tools/m4/csharpexec-test.exe which doesn't have source code (C# is effectively proprietary anyway). Did sys-devel/gettext: deblob to fix it.

TypeScript

Compiler itself is written in TypeScript, no bootstrap path possible as the commit introducing the compiler is TypeScript code. Want TypeScript compiler? Get a blob from npmjs.org, like the Initial commit tells you.

Alternative might be swc (Rust). Note that Deno (also Rust) just grabs pre-transpiled JS from Microsoft and Babel simply seems to depend on the typescript package.
And it should be noted that TypeScript seems to have no specification anymore. (Commit: Remove doc folder (old archived spec and assets), word2md script)

Dart

Yet another chicken-egg language without a single documented way to bootstrap it from source, I wish they would have learned from the other language from Google: Go.

rollup

chicken-egg: Uses rollup to build itself
one-step circular dependency: rollup → acorn → rollup
links to a two-step circular dependency: rollup → eslint → webpack → acorn → eslint

I guess web development can also mean creating cyclic graphs of dependencies.
Note: acorn doesn't lists it's dependencies on npmjs because it publishes a pre-compiled version…

Potentially problematic

OCaml

Has binary seeds in ./boot, there is camlboot but it seems to be pretty inefficient (takes hours to compile when regular ocaml takes minutes to compile)

Zig

Threw out the C++ implementation in favor of a large WASM binary seed, for now it's chained-bootstrapping, hopefully an alternative compiler written in a bootstrapped language will appear.

Historically problematic

Firefox >=68 <=78

Firefox would bundle python2 and refuse to build if removed. See Debian firefox-esr source history

Non-Problematic / Praise

Go

Installing Go from source in the official Go documentation details it, both GCCGO and a branching out of Go 1.4 are supported.